Help with displacement modifier application with an array modifier for a random result
If you want discontinuities in your displacement map you probably have to either break your object apart and use instances instead each with different texture settings, or apply the array modifier and unwrap each "step" individually then move them around in the UV editor to break the continuity of the UV coordinates.

Either global or local coordinates are bound to generate one seamless displacement map over all chunks of the mush since they are all contiguous.

Alternatively, if you are using the Cycles render engine you could use builtin material based displacement instead, and use an Object Info's Random output and instances to make the texture randomly offset on each separate object.

Edit: You could just use the "Object" texture coordinates on the displace modifier, then use an empty to drive the placement of the texture.

Create two or three different empties and use them alternatingly, that should be enough to achieve a random look. Set up one or two different instances and then you can just copy modifier settings from one object to may others by selecting them all, and selecting the source object last, then pressing Ctrl+L and choosing Link>Modifiers option